
import warnings
warnings.filterwarnings("ignore", category=DeprecationWarning) 

# define GPU for BERT model
import os
os.environ['CUDA_VISIBLE_DEVICES'] = '3'


import pandas as pd
from matplotlib import pyplot as plt
import wordcloud
from sklearn.feature_extraction.text import ENGLISH_STOP_WORDS
import nltk
import spacy
from gensim import corpora
from gensim.models import LsiModel, LdaModel
from gensim.models.callbacks import PerplexityMetric
from tqdm.notebook import tqdm
import pyLDAvis.gensim
import gensim.downloader as api
from gensim.models import Word2Vec
import gensim
import numpy as np
from sklearn.cluster import KMeans
from gensim.models import KeyedVectors
from sklearn.manifold import TSNE
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from bokeh.io import output_notebook
import bokeh.models as bm, bokeh.plotting as pl
from nltk.tokenize import WordPunctTokenizer
from multiprocessing import Pool
from bs4 import BeautifulSoup
import re
from collections import defaultdict
import umap
import hdbscan
from sklearn.cluster import DBSCAN


# from spacy.cli.download import download
# download(model="en_core_web_sm")
# nltk.download('stopwords')


df = pd.read_csv('emails.csv')


df.head(3)


msg = df['message'][0]


print(msg)

Message-ID: <18782981.1075855378110.JavaMail.evans@thyme>
Date: Mon, 14 May 2001 16:39:00 -0700 (PDT)
From: phillip.allen@enron.com
To: tim.belden@enron.com
Subject: 
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
X-From: Phillip K Allen
X-To: Tim Belden <Tim Belden/Enron@EnronXGate>
X-cc: 
X-bcc: 
X-Folder: \Phillip_Allen_Jan2002_1\Allen, Phillip K.\'Sent Mail
X-Origin: Allen-P
X-FileName: pallen (Non-Privileged).pst

Here is our forecast


import email


'Email object keys: %s' % email.message_from_string(msg).keys()

"Email object keys: ['Message-ID', 'Date', 'From', 'To', 'Subject', 'Mime-Version', 'Content-Type', 'Content-Transfer-Encoding', 'X-From', 'X-To', 'X-cc', 'X-bcc', 'X-Folder', 'X-Origin', 'X-FileName']"


def get_text_from_email(msg_text):
    '''To get the content from email objects'''
    
    msg = email.message_from_string(msg_text)
    parts = [part.get_payload() for part in msg.walk() if \
             part.get_content_type() == 'text/plain']
    return ''.join(parts)


get_text_from_email(msg)

'Here is our forecast\n\n '


df['Content'] = list(map(get_text_from_email, df['message']))

messages = list(map(email.message_from_string, df['message']))
for key in ['Date', 'From', 'To', 'Subject']:
    df[key] = [doc[key] for doc in messages]


def split_email_addresses(line):
    '''To separate multiple email addresses'''
    
    if line:
        addrs = line.split(',')
        addrs = frozenset(map(lambda x: x.strip(), addrs))
    else:
        addrs = None
    return addrs


def convert_date(data):
    # https://docs.python.org/3/library/datetime.html#strftime-and-strptime-behavior
    return pd.to_datetime(data).tz_convert(None).strftime('%a %d %b %Y %H:%M:%S')


df['User'] = df['file'].map(lambda x: x.split('/')[0])
df.drop(['file', 'message'], axis=1, inplace=True)
df['From'] = df['From'].map(split_email_addresses)
df['To'] = df['To'].map(split_email_addresses)

df['Date'] = df['Date'].apply(convert_date)
df['Date'] = pd.to_datetime(df['Date'], infer_datetime_format=True)


df.sample(3)


df['Content'].iloc[48]

'---------------------- Forwarded by Phillip K Allen/HOU/ECT on 09/12/2000 \n11:22 AM ---------------------------\n\nMichael Etringer\n\n09/11/2000 02:32 PM\n\nTo: Phillip K Allen/HOU/ECT@ECT\ncc:  \nSubject: Contact list for mid market\n\nPhillip,\nAttached is the list.  Have your people fill in the columns highlighted in \nyellow.  As best can we will try not to overlap on accounts. \n\nThanks, Mike\n\n\n'


def good_word(word):
    for c in word:
        if '0' <= c <= '9':
            return False
        
    return True

def clean_text(text):
    x = text
    text = nltk.RegexpTokenizer('\s+', gaps=True).tokenize(text.lower())
    text = ' '.join([word for word in text if good_word(word)])

    text = re.sub('<.*>', '', text) # text inside <>, some forwarded info
    text = re.sub('\[.*\]', '', text) # text inside [], this is some attachements
    text = re.sub('\S*@\S*\s?', '', text) # remote email addresses
    text = re.sub('\S*/hou/\S*s?', '', text) # some corporation usernames
    text = re.sub('http[s]?://\S+', '', text) # remove links
    text = re.sub('www\.\S+', '', text) # remove links

    
    # text = re.sub('.*subject:', '', text) # remain only text subject [works too long, let's implement]
    
    msg_text = 'subject:'
    idx = text.find(msg_text)
    if idx != -1:
        text = text[idx + len(msg_text):].strip()
    
    return text

for field in ['Content', 'Subject']:
    df[field] = [clean_text(email) for email in df[field]]

<>:10: DeprecationWarning: invalid escape sequence \s
<>:14: DeprecationWarning: invalid escape sequence \[
<>:15: DeprecationWarning: invalid escape sequence \S
<>:16: DeprecationWarning: invalid escape sequence \S
<>:17: DeprecationWarning: invalid escape sequence \S
<>:18: DeprecationWarning: invalid escape sequence \.
<>:10: DeprecationWarning: invalid escape sequence \s
<>:14: DeprecationWarning: invalid escape sequence \[
<>:15: DeprecationWarning: invalid escape sequence \S
<>:16: DeprecationWarning: invalid escape sequence \S
<>:17: DeprecationWarning: invalid escape sequence \S
<>:18: DeprecationWarning: invalid escape sequence \.
<ipython-input-16-18790927da10>:10: DeprecationWarning: invalid escape sequence \s
  text = nltk.RegexpTokenizer('\s+', gaps=True).tokenize(text.lower())
<ipython-input-16-18790927da10>:14: DeprecationWarning: invalid escape sequence \[
  text = re.sub('\[.*\]', '', text) # text inside [], this is some attachements
<ipython-input-16-18790927da10>:15: DeprecationWarning: invalid escape sequence \S
  text = re.sub('\S*@\S*\s?', '', text) # remote email addresses
<ipython-input-16-18790927da10>:16: DeprecationWarning: invalid escape sequence \S
  text = re.sub('\S*/hou/\S*s?', '', text) # some corporation usernames
<ipython-input-16-18790927da10>:17: DeprecationWarning: invalid escape sequence \S
  text = re.sub('http[s]?://\S+', '', text) # remove links
<ipython-input-16-18790927da10>:18: DeprecationWarning: invalid escape sequence \.
  text = re.sub('www\.\S+', '', text) # remove links


df['Content'].iloc[48]

'contact list for mid market phillip, attached is the list. have your people fill in the columns highlighted in yellow. as best can we will try not to overlap on accounts. thanks, mike'


sentence_lengths = [min(500, len(s.split())) for s in df['Content']]

cnt = 0
for x in sentence_lengths:
    if x == 500:
        cnt += 1
        
        
print('There are %s sentences with length >= 500' % cnt)

plt.figure(figsize=(11, 5))
plt.hist(sentence_lengths, bins=30, color='green')
plt.xlabel('Количество слов в письмах', fontsize=18)
plt.ylabel('Количество писем', fontsize=18)
plt.xlim(0, 400)
plt.show()

There are 34516 sentences with length >= 500


ax = df.groupby(df['Date'].dt.year)['Content'].count().plot(xlim=(1995, 2005), grid=True)
ax.set_xlabel('Year', fontsize=18)
ax.set_ylabel('N emails', fontsize=18)

Text(0, 0.5, 'N emails')


ax = df.groupby(df['Date'].dt.dayofweek)['Content'].count().plot(grid=True)
ax.set_xlabel('Day of week', fontsize=15)
ax.set_ylabel('N emails', fontsize=15)

Text(0, 0.5, 'N emails')


ax = df.groupby(df['Date'].dt.hour)['Content'].count().plot(grid=True)
ax.set_xlabel('Hour', fontsize=18)
ax.set_ylabel('N emails', fontsize=18)

Text(0, 0.5, 'N emails')


def plot_wordcloud(text):
    fig, ax = plt.subplots(figsize=(16, 10))
    wc = wordcloud.WordCloud(width=1200, 
                             height=750, 
                             max_words=200,
                             stopwords=list(ENGLISH_STOP_WORDS),
                             background_color='white').generate(text)
    ax.imshow(wc)
    ax.axis("off")
    # print(wc.words_)


subjects = ' '.join(df['Subject'])
plot_wordcloud(subjects)


contents = ' '.join(df.sample(5000)['Content'])
plot_wordcloud(contents)


cnt = defaultdict(int) 
for item in df['From']:
    sender = list(item)[0]
    # sender = sender[:sender.rfind('.')]
    cnt[sender] += 1


users, counts = zip(*sorted(cnt.items(), key=lambda x: x[1], reverse=True)[:20])


plt.figure(figsize=(11, 5))
plt.barh(range(20), counts, align='center', color='green', alpha=0.8)
plt.yticks(range(20), users, fontsize=15)
plt.show()


bad_cnt = 0
for item in df['To']:
    if item is None:
        bad_cnt += 1
        continue
        
    for receiver in item:
        # receiver = x[:x.rfind('.')]
        cnt[receiver] += 1
print('There is %s emails without receivers' % bad_cnt)

There is 21847 emails without receivers


users, counts = zip(*sorted(cnt.items(), key=lambda x: x[1], reverse=True)[:20])


plt.figure(figsize=(11, 5))
plt.barh(range(20), counts, align='center', color='green', alpha=0.8)
plt.yticks(range(20), users, fontsize=15)
plt.show()


sub_df = df[['From', 'To', 'Date']].dropna()
print(sub_df.shape)

# drop emails sending to multiple addresses
sub_df = sub_df.loc[sub_df['To'].map(len) == 1]
print(sub_df.shape)

(495554, 3)
(354600, 3)


sub_df = sub_df.groupby(['From', 'To']).count().reset_index()

# unpack frozensets
sub_df['From'] = sub_df['From'].map(lambda x: next(iter(x)))
sub_df['To'] = sub_df['To'].map(lambda x: next(iter(x)))

# rename column
sub_df.rename(columns={'Date': 'count'}, inplace=True)
sub_df.sort_values('count', ascending=False).head(10)


import networkx as nx

G = nx.from_pandas_edgelist(sub_df, 'From', 'To', edge_attr='count', create_using=nx.DiGraph())
print('Number of nodes: %s, Number of edges: %s' % (G.number_of_nodes(), G.number_of_edges()))

Number of nodes: 25396, Number of edges: 56144


fig, (ax1, ax2) = plt.subplots(1,2, figsize=(11, 5))
ax1.hist(list(dict(G.in_degree(weight='count')).values()), log=True, bins=20, color='green')
ax1.set_xlabel('Степень входа вершин', fontsize=18)

ax2.hist(list(dict(G.out_degree(weight='count')).values()), log=True, bins=20, color='green')
ax2.set_xlabel('Степень выхода вершин', fontsize=18)

Text(0.5, 0, 'Степень выхода вершин')


comp_sizes = []
for nodes in nx.connected_components(G.to_undirected()):
    comp_sizes.append(len(nodes))
    
print('There are %s connected components' % len(comp_sizes))

comp_sizes = np.array(comp_sizes)

cnt = defaultdict(int)
for x in comp_sizes:
    cnt[x] += 1
    
keys = list(cnt.keys())
values = list(cnt.values())

order = np.argsort(values)[::-1]
keys = np.array(keys)[order]
values = np.array(values)[order]

plt.figure(figsize=(11, 5))
plt.barh(range(len(keys)), values, color='green', log=True, )
plt.yticks(range(len(keys)), keys, fontsize=15)
plt.ylabel('Размер компоненты связности', fontsize=18)
plt.xlabel('Количество', fontsize=18)
plt.show()

There are 1430 connected components


df = df.head(50000)


def normalize(word):
    return nlp(word)[0].lemma_


nlp = spacy.load("en_core_web_sm")
normalize('dogs'), normalize('playing')

('dog', 'play')


emails = list(df['Content'])
emails = [nltk.RegexpTokenizer(r'\w+').tokenize(email.lower()) for email in emails]


def only_eng_chars(word):
    for c in word:
        if c > 'z' or c < 'a':
            return False
    return True


def f(email_words):
    return [normalize(word) for word in email_words if word not in stop_words and len(word) > 2 and only_eng_chars(word)]


stop_words = set(nltk.corpus.stopwords.words('english'))

n_cpu = 70
with Pool(n_cpu) as p:
    emails = p.map(f, emails)

emails = [email_words for email_words in emails if len(email_words) > 2]
print(f'Total emails extracted: {len(emails)}')

Total emails extracted: 47389


dictionary = corpora.Dictionary(emails)
corpus = [dictionary.doc2bow(email_words) for email_words in emails]


def f(num_topics):
    perplexity_logger = PerplexityMetric(corpus=corpus, logger='shell')

    lda = LdaModel(corpus, id2word=dictionary, num_topics=num_topics, callbacks=[perplexity_logger],
                   iterations=200, passes=10)

    return perplexity_logger.get_value()
    
rng = range(3, 10)
n_cpu = len(rng)
with Pool(n_cpu) as p:
    pps = p.map(f, rng)


plt.figure(figsize=(9, 6))
plt.plot(rng, pps)
plt.xlabel('Num topics')
plt.ylabel('Perplexity')
plt.title('Perplexity dependent by number of topics')
plt.grid()
plt.show()


def show(model):
    str_topics = [topic_w for topic_number, topic_w in model.print_topics()]
    str_topics_split = list(map(lambda x: x.split("+"), str_topics))
    str_topics_split = [list(map(lambda x: x.split("*")[1].strip()[1:-1], elem)) for elem in str_topics_split]
    for topic in str_topics_split:
        print(', '.join(topic))


best_num_topics = rng[np.argmin(pps)]
lda = LdaModel(corpus, id2word=dictionary, num_topics=best_num_topics, iterations=200, passes=10)


show(lda)

page, com, mail, please, new, click, order, free, receive, email
please, enron, meet, thank, time, schedule, contact, attach, information, report
get, know, send, subject, would, thank, week, message, let, think
enron, company, market, page, would, state, issue, say, year, price


data_lda = pyLDAvis.gensim.prepare(lda, corpus, dictionary)
pyLDAvis.enable_notebook()
pyLDAvis.display(data_lda)


path = api.load("glove-twitter-50", return_path=True)


model = KeyedVectors.load_word2vec_format(path)


model_2 = Word2Vec(size=50, min_count=1)
model_2.build_vocab(emails)
total_examples = model_2.corpus_count
model_2.build_vocab([list(model.vocab.keys())], update=True)
model_2.intersect_word2vec_format(path)


model_2.train(emails, total_examples=total_examples, epochs=5)

(22711105, 22718550)


words = np.array(list(set((" ".join([" ".join(x) for x in emails])).split())))


word_vectors = []
bad_count = 0

for x in words:
    try:
        vec = model_2.wv.get_vector(x)
    except KeyError:
        bad_count += 1
        vec = np.zeros(50)
    word_vectors.append(vec)
    
print('There are %s words from %s without embeddings' % (bad_count, len(words)))

There are 0 words from 49183 without embeddings


word_vectors = umap.UMAP(n_components=5).fit_transform(word_vectors)


word2vec_map = dict()
for i, word in enumerate(words):
    word2vec_map[word] = word_vectors[i]


sentence_vectors = []

for email in emails:
    vec = np.zeros(5)
    for word in email:
        # no exception, all words have embeddings
        vec += word2vec_map[word]
    vec /= len(email)
    sentence_vectors.append(vec)


hdbscan_ = hdbscan.HDBSCAN(min_cluster_size=7, core_dist_n_jobs=70)
hdbscan_.fit(sentence_vectors)


labels = sorted(set(hdbscan_.labels_))
print('There are %s clusters' % len(labels))

There are 1335 clusters


cluster_vectors = []

sentence_vectors = np.array(sentence_vectors)
# first cluster in outliers
for label in labels[1:]:
    vec = np.mean(sentence_vectors[hdbscan_.labels_ == label], axis=0)
    cluster_vectors.append(vec)
cluster_vectors = np.array(cluster_vectors)


cluster_vectors.shape, word_vectors.shape

((1334, 5), (49183, 5))


def show_cluster(num, cluster_size=10):
    dists = np.sum((word_vectors - cluster_vectors[num]) ** 2, axis=1)
    order = np.argsort(dists)[:cluster_size]
    print(words[order])


# 3, 54, 157, 108, 110, 194


show_cluster(110)

['text' 'follow' 'txt' 'plz' 'reply' 'pls' 'please' 'repeat' 'anniversary'
 'surprise']


show_cluster(54)

['angel' 'queen' 'princess' 'prince' 'savage' 'poetic' 'explicit' 'remix'
 'prod' 'barbie']


show_cluster(3)

['hawaii' 'disneyland' 'jamaica' 'alaska' 'beach' 'resort' 'skyline'
 'harbor' 'atlantic' 'caribbean']


show_cluster(194)

['satisify' 'vain' 'endless' 'definition' 'quite' 'priceless' 'compete'
 'successfully' 'separate' 'genius']


show_cluster(157)

['heterosexual' 'irresistible' 'homosexual' 'visible' 'invisible'
 'singular' 'peculiar' 'plural' 'neutral' 'favorable']


show_cluster(108)

['teen' 'interracial' 'wannabe' 'lesbian' 'amateur' 'porn' 'ebony' 'sex'
 'anal' 'cougar']


word_vectors_umap = umap.UMAP(n_components=2).fit_transform(word_vectors)

# word_vectors_pca = TSNE(n_components=2, n_jobs=40).fit_transform(word_vectors)
# word_vectors_pca = PCA(n_components=2).fit_transform(word_vectors)

word_vectors_umap = StandardScaler().fit_transform(word_vectors_umap)

output_notebook()

def draw_vectors(x, y, radius=10, alpha=0.25, color='blue',
                 width=600, height=400, show=True, **kwargs):
    """ draws an interactive plot for data points with auxilirary info on hover """
    if isinstance(color, str): color = [color] * len(x)
    data_source = bm.ColumnDataSource({ 'x' : x, 'y' : y, 'color': color, **kwargs })

    fig = pl.figure(active_scroll='wheel_zoom', width=width, height=height)
    fig.scatter('x', 'y', size=radius, color='color', alpha=alpha, source=data_source)

    fig.add_tools(bm.HoverTool(tooltips=[(key, "@" + key) for key in kwargs.keys()]))
    if show: pl.show(fig)
    return fig

draw_vectors(word_vectors_umap[:, 0], word_vectors_umap[:, 1], token=words)


model_2.wv.most_similar('russia')

[('ukraine', 0.8960039019584656),
 ('canada', 0.8308505415916443),
 ('russian', 0.8201991319656372),
 ('electricite', 0.814449667930603),
 ('sweden', 0.8108468651771545),
 ('moscow', 0.8099092245101929),
 ('greece', 0.8071787357330322),
 ('norway', 0.8041681051254272),
 ('zealand', 0.8002776503562927),
 ('belgium', 0.7978895902633667)]


model_2.wv.most_similar(positive=['queen', 'boy'], negative=['girl'])

[('king', 0.8481787443161011),
 ('prince', 0.847251296043396),
 ('angel', 0.8389350175857544),
 ('lady', 0.8351561427116394),
 ('aka', 0.8251813650131226),
 ('punk', 0.8228825926780701),
 ('princess', 0.8196807503700256),
 ('rock', 0.7763223648071289),
 ('band', 0.7758490443229675),
 ('monster', 0.7747203707695007)]


from bertopic import BERTopic

/usr/local/lib/python3.8/dist-packages/packaging/version.py:127: DeprecationWarning: Creating a LegacyVersion has been deprecated and will be removed in the next major release
  warnings.warn(


emails_bert = list(df['Content'])
len(emails_bert)

50000


def tokenize(x):
    return ' '.join(nltk_tokenizer.tokenize(x))

nltk_tokenizer = WordPunctTokenizer()


emails_bert = [tokenize(email) for email in emails_bert]


topic_model = BERTopic()
topics, _ = topic_model.fit_transform(emails_bert)


def show_topic(num):
    return [x[0] for x in topic_model.get_topic(num) if x[1] > 0]


show_topic(366)

['prick', 'sucks', 'terrible', 'yellowpages', 'dirty', 'bad', 'dislike']


show_topic(261)

['congrats', 'congratulations', 'exciting', 'promotions', 'jeff']


show_topic(327)

['superstar',
 'choate',
 'wonderful',
 'success',
 'gifts',
 'huge',
 'nice',
 'informative',
 'kimberly',
 'glad']


show_topic(1164)

['drop',
 'pick',
 'damon',
 'butch',
 'dropping',
 'picking',
 'richie',
 'rid',
 'neal',
 'kirby']


show_topic(394)

['vpn',
 'pending',
 'applications',
 'requested',
 'id',
 'natgas',
 'jeffrey',
 'phillip',
 'application',
 'jeff']


topic_model.visualize_topics()


topic_sizes = np.array(topic_model.get_topic_freq()['Count'])


print('There are %s topics' % len(topic_sizes))

There are 1750 topics


th = 80
print('There are %s topics with size > %s' % (np.sum(topic_sizes > th), th))


plt.figure(figsize=(11, 5))
plt.hist(topic_sizes[topic_sizes <= th], bins=30, color='green')
plt.xlabel('Размер темы', fontsize=18)
plt.ylabel('Количество тем', fontsize=18)
plt.show()

There are 13 topics with size > 80

	file	message
0	allen-p/_sent_mail/1.	Message-ID: <18782981.1075855378110.JavaMail.e...
1	allen-p/_sent_mail/10.	Message-ID: <15464986.1075855378456.JavaMail.e...
2	allen-p/_sent_mail/100.	Message-ID: <24216240.1075855687451.JavaMail.e...

	Content	Date	From	To	Subject	User
472472	---------------------- Forwarded by Mark Taylo...	2000-01-17 15:27:00	(mark.taylor@enron.com)	(mark.haedicke@enron.com)	Credit Trading OnLine - Results of Legal Due D...	taylor-m
46559	MY RECORD SHOULD BE 8 AND 2	2000-11-07 08:02:00	(mike.carson@enron.com)	(rgibbs@btubrokers.com)	Re: Week 10 Results	carson-m
131158	I'm going through the Jan transport invoices. ...	2000-04-05 12:05:00	(chris.germany@enron.com)	(brenda.fletcher@enron.com, sherry.anastas@enr...	Jan Transport	germany-c

	From	To	count
17908	pete.davis@enron.com	pete.davis@enron.com	9141
38033	vince.kaminski@enron.com	vkaminski@aol.com	4308
28920	enron.announcements@enron.com	all.worldwide@enron.com	2206
28935	enron.announcements@enron.com	all.houston@enron.com	1701
26510	kay.mann@enron.com	suzanne.adams@enron.com	1528
38031	vince.kaminski@enron.com	shirley.crenshaw@enron.com	1190
14564	steven.kean@enron.com	maureen.mcvicker@enron.com	1014
26309	kay.mann@enron.com	nmann@erac.com	980
18926	kate.symes@enron.com	evelyn.metoyer@enron.com	915
18930	kate.symes@enron.com	kerri.thompson@enron.com	859

Набор данных электронной почты Enron Corporation¶

Чтобы вручную такое не парсить, будем использовать библиотеку email¶

Пример письма до чистки текста:¶

Пример письма после чистки текста:¶

Теперь посмотрим на распределение длин писем (по количеству слов)¶

Когда люди отсылали письма?¶

О чём говорится в письмах?¶

В темах писем¶

В содержании писем¶

Анализ отправителей и получателей писем¶

Топ-20 адресов, с которых было отправлено наибольшее количество электронных писем¶

Топ-20 адресов, на которые было отправлено наибольшее количество электронных писем¶

Как видим, в графиках распределения получателей и отправителей писем много различий - какие-то люди писем меньше пишут, чем получают и наоборот¶

Как видим, некоторые люди отправляют себе много электронных писем¶

Интересно посмотреть на эти взаимосвязи в виде графа¶

Тематическое моделирование c LDA model¶

Для начала слова нормализуем и удалим оставшиеся знаки препинания¶

Интерпретируемости получили не очень много, LDA модель сработала не очень хорошо¶

Кластеризация word2vec embeddings¶

Понизим размерность до 5 с помощью UMAP¶

Будем считать кластеры не для слов, а для усредненных эмбеддингов текстов (писем). В этом случае для интерпретации будем брать слова наиболее близкие к кластеру.¶

Интересный кластер, хоть некоторые слова написаны по-разному, модель смогла понять что они встречаются в похожих контекстах:¶

Кластер некоторых интересный личностей:¶

Кластер некоторых стран и континентов:¶

Кластер радостных слов:¶

А также ещё некоторые¶

Теперь попробуем другой подход, кластеризуем просто векторные представления слов¶

Тематическое моделирование c BERTopic¶

Кластере в среднем более интерпретируемы, чем ранее¶